We consider new parameterization schemes for the extra transport velocity by eddies in a stratified fluid, with particular emphasis on baroclinic instability. These come in the form of elliptic equations, previously unmentioned, which we derive for the eddy-induced overturning stream function. They guarantee decrease of the mean field potential energy. Our principal example gives a relationship between the vertical shear of the overturning velocity and the buoyancy torque of the main geostrophic current. The parameterized velocity is nonsingular at the bottom and the sea surface, contrasting with previous constant-coefficient theories based on depth diffusion. Idealized two-dimensional numerical experiments successfully reproduce meridional overturning circulation even when the background density gradient is uniform everywhere (the Eady problem) or when the bottom is steeply sloped. We further demonstrate that adding an eddy form drag (wave stress) term in the TRM momentum equations yields overturning of the velocity field.